Multi-objective optimization of the two-stage helical gearbox with tribological constraints

Abstract

In this study, a novel multi-objective optimization of a two-stage helical gearbox is carried out with a comprehensive range of constraints. Two objective functions are formulated, the first minimizes the volume and the second minimizes the total power loss in the gearbox. Various design constraints such as bending stress, pitting stress, etc., and tribological constraints namely, scuffing and wear are included. By using a specially formulated discrete version of Non-Dominated Sorting Genetical Algorithm II (NSGA-II) these objective functions are minimized for three different gear profiles (unmodified profile, smooth meshing profile and high load capacity profile) and four ISO oil grades and at two speeds. The results are compared with standard single objective minimization without tribological constraints as per existing literature and single objective minimization with tribological constraints. It is shown that there is a high probability of wear failure for solutions obtained from single objective minimization without tribological constraints and the total power loss of the gearbox is reduced by half when using the multi-objective approach. Multi-objective optimization was also shown to give lower power losses when compared to the case of single objective optimization with tribological constraints.